Abstract

We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators, we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electro-oxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.

Received 18 October 2013Accepted 16 December 2013Published online 08 January 2014

Lead Paragraph: In the 17th century, Christiaan Huygens was the first who encountered the phenomenon of synchronization, when watching two coupled pendulum clocks adjusting their oscillation phase to each other. Since then, a variety of systems exhibiting synchronization were studied, e.g., the flashing of fireflies or networks of pacemaker cells keeping our heart beating in time. In these systems, the key aspect is that nonidentical oscillating elements, as nature is never perfect, with a distribution of natural frequencies become synchronized due to the mutual coupling. In contrast, in 2002, Kuramoto and Battogtokh1 found the opposite phenomenon: a perfect symmetric system of identical oscillators coupled via a nonlocal coupling (i.e., a coupling that somehow decreases with the distance between two oscillators) may undergo a transition to a state, where a synchronized group of oscillators coexists with an unsynchronized one. This situation was later named chimera state, since the chimera was, according to Greek mythology, composed of the parts of different animals. The nonlocality of the coupling is believed to be indispensable for the formation of chimera states. However, in the present article, we show that this is a misbelief, as we found chimera states under solely global coupling. Global coupling means that each individual oscillator couples to the mean field of all oscillators. In our case, the mean field is a nonlinear function of the state variables of each oscillator.

Acknowledgments:

We thank Andreas Heinrich and Martin Wiegand for assistance on the experiments and Moritz Müller for his work on the simulation program. Financial support from the Deutsche Forschungsgemeinschaft (Grant No. KR1189/12-1), the Institute for Advanced Study, Technische Universität München funded by the German Excellence Initiative and the cluster of excellence Nanosystems Initiative Munich (NIM) is gratefully acknowledged.

Article outline:I. INTRODUCTIONII. RESULTS AND DISCUSSIONA. Chimera states in an ensemble of Stuart-Landau oscillatorsB. Transition to a chimera state in the modified CGLEC. Experimental validation of theoretical predictionIII. CONCLUSIONS